Factor 9 grid: Difference between revisions

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== Factor 9 Grid temperament (495 & 666) ==

In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of 666 equal divisions of the octave. If performed using general temperament theory, it results in the following 23-limit temperament:

Subgroup: 2.3.5.7.11.13.17.19.23

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The motivation behind the scale, or any kind of esoteric just intonation proposal, is that the irrational pitch standard of equal temperament has an acoustically unpleasant effect, that subsequently allegedly spreads to the subconscious part of the mind and results in degradation of the quality of life.

However, it is not possible to have both the rationality of just intonation and evenness of equal temperament at the same time. The irrationality of equal temperament has been known since ancient times by various names, the most common being the proof by infinite descent of the square root of two. For example if a stack of fifths (3/2) were to close at the octave, it would imply the existence of an even power of 3, which is nonsense.

However, it is not possible to have both the rationality of just intonation and evenness of equal temperament at the same time. The irrationality of equal temperament has been known since ancient times by various names, the most common being the proof by infinite descent of the square root of two. If there was an exact JI interval fraction which corresponds to the 600 cent tritone, it's numerator and denominator would have to be both even and coprime, which cannot happen. For example if a stack of fifths (3/2) were to close at the octave, it would imply the existence of an even power of 3, which is nonsense.

If there is credible scientific evidence that playing just intonation music through public loudspeakers, in soundtracks, or other public venues will increase peace and quality of human life, it must be presented properly, without occultist context.

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 == Factor 9 Grid temperament (495 & 666) ==
 In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of 666 equal divisions of the octave. If performed using general temperament theory, it results in the following 23-limit temperament:
 Subgroup: 2.3.5.7.11.13.17.19.23
@@ Line 57: / Line 58: @@
 The motivation behind the scale, or any kind of esoteric just intonation proposal, is that the irrational pitch standard of equal temperament has an acoustically unpleasant effect, that subsequently allegedly spreads to the subconscious part of the mind and results in degradation of the quality of life.
-However, it is not possible to have both the rationality of just intonation and evenness of equal temperament at the same time. The irrationality of equal temperament has been known since ancient times by various names, the most common being the proof by infinite descent of the square root of two. For example if a stack of fifths (3/2) were to close at the octave, it would imply the existence of an even power of 3, which is nonsense.
+However, it is not possible to have both the rationality of just intonation and evenness of equal temperament at the same time. The irrationality of equal temperament has been known since ancient times by various names, the most common being the proof by infinite descent of the square root of two. If there was an exact JI interval fraction which corresponds to the 600 cent tritone, it's numerator and denominator would have to be both even and coprime, which cannot happen. For example if a stack of fifths (3/2) were to close at the octave, it would imply the existence of an even power of 3, which is nonsense.
 If there is credible scientific evidence that playing just intonation music through public loudspeakers, in soundtracks, or other public venues will increase peace and quality of human life, it must be presented properly, without occultist context.